Imaginary Number Manipulations

Date: 7/10/96 at 18:59:48
From: Anonymous
Subject: Imaginary Number Manipulations
Hi, Dr. Math!
I have recently been doing some manipulations with the imaginary
number (i), and in some of them negative (i) seems to "turn into"
positive (i). Consider the situation below:
1.5 3/2 3
-i = -1 x square root(-1) = (-1) = (-1) = square root((-1) ) =
square root(-1) = i
For some reason, a factor of -1 disappears, resulting in the seemingly
absurd equation -i = i. I have tried to find a mistake in the above,
but found none (unless some fundamental rules are different for
imaginary numbers). I am also wondering if there is a rule that
states that (i) cannot be renamed as the square root of -1, although
the two are (supposed to be) equal. Do you know what is going on
here?
Artem Gleyzer

Date: 7/10/96 at 20:39:42
From: Doctor Anthony
Subject: Re: Imaginary Number Manipulations
The square root of (-1) is +or- i
consider (+i)*(+i) = i^2 = -1
and (-i)*(-i) = i^2 = -1
When you take square roots in an equation, you will in general have to
consider that one of your 'solutions' may be wrong.
One relationship worth remembering is that 1/i = -i
-Doctor Anthony, The Math Forum
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